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Springer, Lecture Notes in Computer Science, p. 360-374, 2005

DOI: 10.1007/978-3-540-31815-6_29

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Hyperelliptic Curve Coprocessors on a FPGA

Proceedings article published in 2004 by HoWon Kim, Thomas J. Wollinger, YongJe Choi, KyoIl Chung, Christof Paar
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Cryptographic algorithms are used in a large variety of dif- ferent applications to ensure security services. It is, thus, very interest- ing to investigate various implementation platforms. Hyperelliptic curve schemes are cryptographic primitives to which a lot of attention was recently given due to the short operand size compared to other algo- rithms. They are speciflcally interesting for special-purpose hardware. This paper provides a comprehensive investigation of high-e-cient HEC architectures. We propose a genus-2 hyperelliptic curve cryptographic coprocessor using a-ne coordinates. We implemented a special class of hyperelliptic curves, namely using the parameter h(x) = x and f = x5 + f1x + f0 and the base fleld GF(289). In addition, we only consider the most frequent case in our implementation and assume that the other cases are handled, e.g. by the protocol. We provide three difierent implementations ranging from high speed to moderate area. Hence, we provide a solution for a variety of applications. Our high performance HECC coprocessor is 78:5% faster than the best previous implementation and our low area implementation utilizes only 22:7% of the area that the smallest published design uses. Taking into account both area and latency, our coprocessor is an order of magnitude more e-cient than previous implementations. We hope that the work at hand provides a step towards introducing HEC systems in practical applications.